Answer: One of the many benefits of a natural mulch such as wood is that it naturally feeds the soil as it decomposes over time. Some important elements of that decomposition process are bacteria and fungi which tend to be most active during wet weather, as you have discovered. In general, while they may look truly awful and disgusting, they are not usually harmful to plants or people (unless ingested).
The possible exception to this is the artillery fungus, but that is only because it may leave stains on hard surfaces such as a car or house siding. Based on your description, though, it sounds like you have some basically harmless slime mold. You might like to look at the photographs and information about some common types at this web site:
I am not aware of any control measure for these. You might try fluffing the mulch to allow the top layer to dry out, or if the appearance really bothers you, you might consider replacing the mulch with a different material such as leaf mold or straw or perhaps an inorganic mulch such as an air and water permeable landscape fabric topped with gravel. Otherwise, once things dry out a bit the mold should recede somewhat.
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